Meta’s Prophet forcasting System

CO2 Time Series

The co2 data set I’m analysing contains measurements of atmospheric carbon dioxide concentrations from 1959 to 1997 which were obtained at Mauna Loa Observatory monthly.

In this Project I’ll be using the Meta’s Prophet system to forecast future atmospheric CO2 concentrations based on historical data. Also to identify seasonal patterns which The Prophet package will model, such as annual and monthly fluctuations.This can help environmental researchers and climate scientists forecast future CO2 levels.

library(prophet)
## Warning: package 'prophet' was built under R version 4.3.3
## Loading required package: Rcpp
## Warning: package 'Rcpp' was built under R version 4.3.3
## Loading required package: rlang
co2.df = data.frame(
  ds=zoo::as.yearmon(time(co2)), 
  y=co2)
co2_model= prophet::prophet(co2.df, weekly.seasonality = TRUE, daily.seasonality = TRUE)
#include weeklyseasonality part
co2_FutureData= prophet::make_future_dataframe(co2_model, periods=8, freq="quarter")
co2_forecast = predict(co2_model, co2_FutureData)
plot(co2_model,co2_forecast)

The plot above is a time series of atmospheric concentrations of CO2 from Jan 1959 till Dec 1999. The dots are actual values observed, but the line is the predicted values. The chart shows an increase in CO2 through the years.

Sesonality

prophet_plot_components(co2_model,co2_forecast)

A constant increase in the levels of CO2 can be seen as the the years pass in the first plot. On the second Graph atmospheric concentrations of CO2 are higher at the beginning of the week but start to decrease until they reach their lowest levels on Tuesday. Then go back up on Wednesday until Thursday, but then decrease again. Daily it can be seen that the lowest concentrations are between the hours 2-22 but are at its highest between 23-1. Between 2-22 the levels fluctuate between -0.05 and 0.

Dygraph

dyplot.prophet(co2_model, co2_forecast)
## Warning: `select_()` was deprecated in dplyr 0.7.0.
## ℹ Please use `select()` instead.
## ℹ The deprecated feature was likely used in the prophet package.
##   Please report the issue at <https://github.com/facebook/prophet/issues>.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

The dygraph above is interactive, so we can zoom in and out and select specific time ranges. This allows for a more detailed exploration of the CO2 data

Regression

co2_lm <- lm(co2 ~ time(co2))
summary(co2_lm)
## 
## Call:
## lm(formula = co2 ~ time(co2))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.0399 -1.9476 -0.0017  1.9113  6.5149 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -2.250e+03  2.127e+01  -105.8   <2e-16 ***
## time(co2)    1.308e+00  1.075e-02   121.6   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.618 on 466 degrees of freedom
## Multiple R-squared:  0.9695, Adjusted R-squared:  0.9694 
## F-statistic: 1.479e+04 on 1 and 466 DF,  p-value: < 2.2e-16

The linear regression provides insights into the relationship between time (independent variable) and CO2 concentrations (dependent variable).

The coefficient estimate for time(co2) is 1.308, suggesting that CO2 concentrations increase by approximately 1.308 ppm per year.

Both the intercept and time(co2) coefficient have small p-values, suggesting that they are statistically significant predictors of CO2 concentrations.

The R-squared value is 96.95% This suggests a strong linear relationship between time and CO2 concentrations.

Overall, the results indicate a strong positive linear relationship between time and CO2 concentrations.

Using Plotly

library(plotly)
## Warning: package 'plotly' was built under R version 4.3.3
## Loading required package: ggplot2
## Warning: package 'ggplot2' was built under R version 4.3.3
## 
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
## 
##     last_plot
## The following object is masked from 'package:stats':
## 
##     filter
## The following object is masked from 'package:graphics':
## 
##     layout
scatter_plot <- plot_ly(data = co2.df, x = ~time(co2), y = ~co2, type = "scatter", mode="line", name = "CO2")

scatter_plot

Air Passengers Time Series

The AirPassengers data is monthly totals of international airline passengers from 1949 to 1960 in thousands

I’ll be using the Meta’s Prophet system to forecast future air passengers traffic based on historical data. I’ll also be identifying seasonal patterns.

AirPassengers.df = data.frame(
  ds=zoo::as.yearmon(time(AirPassengers)), 
  y=AirPassengers)

AirPassengers_model= prophet::prophet(AirPassengers.df, weekly.seasonality = TRUE, daily.seasonality = TRUE )

AirPassengers_FutureData = prophet::make_future_dataframe(AirPassengers_model, periods=17, freq="quarter")

AirPassengers_forecast= predict(AirPassengers_model, AirPassengers_FutureData)

plot(AirPassengers_model,AirPassengers_forecast)

The time series above shows the number of Airline passengers in thousands from Jan 1949 to Mar 1965. The dots are actual values, and the line is predicted values.

I made the period 17 in the code to predict an extra 4 years and three months.

Sesonality

prophet_plot_components(AirPassengers_model,AirPassengers_forecast)

These plots include yearly, weekly and daily seasonality.

Weekly the lowest amount of passengers are on Tuesday and the highest amount is on Friday.

Yearly the passengers fluctuate but peak in July and August.

Dygraph

dyplot.prophet(AirPassengers_model, AirPassengers_forecast)

Regression

AirPassengers_lm <- lm(AirPassengers ~ time(AirPassengers))
summary(AirPassengers_lm)
## 
## Call:
## lm(formula = AirPassengers ~ time(AirPassengers))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -93.858 -30.727  -5.757  24.489 164.999 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         -62055.907   2166.077  -28.65   <2e-16 ***
## time(AirPassengers)     31.886      1.108   28.78   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 46.06 on 142 degrees of freedom
## Multiple R-squared:  0.8536, Adjusted R-squared:  0.8526 
## F-statistic: 828.2 on 1 and 142 DF,  p-value: < 2.2e-16

The intercept coefficient is -62055.907 and the coefficient for time is 31.886, which shows that the number of AirPassengers increases by 31.886 passengers per month.

The R-squared value indicates that 85.36% of the variance in AirPassenger numbers is explained by the linear regression model.

Overall, the regression model suggests a strong positive linear relationship between time and the number of AirPassengers.